Information on Result #1433384
Linear OOA(4240, 16443, F4, 2, 43) (dual of [(16443, 2), 32646, 44]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4240, 16443, F4, 43) (dual of [16443, 16203, 44]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4239, 16441, F4, 43) (dual of [16441, 16202, 44]-code), using
- construction X applied to C([0,21]) ⊂ C([0,17]) [i] based on
- linear OA(4225, 16385, F4, 43) (dual of [16385, 16160, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(4183, 16385, F4, 35) (dual of [16385, 16202, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(414, 56, F4, 7) (dual of [56, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- a “GraXX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- construction X applied to C([0,21]) ⊂ C([0,17]) [i] based on
- linear OA(4239, 16442, F4, 42) (dual of [16442, 16203, 43]-code), using Gilbert–Varšamov bound and bm = 4239 > Vbs−1(k−1) = 74008 836139 471852 670836 970369 953337 522593 116264 711287 047793 690984 425403 372905 926471 688005 136467 245376 906835 280597 840796 933913 930751 227257 789352 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(4239, 16441, F4, 43) (dual of [16441, 16202, 44]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(4240, 8221, F4, 3, 43) (dual of [(8221, 3), 24423, 44]-NRT-code) | [i] | OOA Folding | |